射流破碎的线性不稳定性分析方法
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摘要
线性不稳定性分析是目前处理柱状射流及复合射流破碎的最常用理论方法之一。该方法基于流体力学基本方程和边界条件,利用线化小扰动法和正则模法开展相关研究,能够成功预测实验中发现的不同流动现象和规律。线化小扰动法的原理是将非线性问题中涉及的物理量分解成零阶近似和小扰动,代入原非线性方程并略去高阶小量,从而使非线性问题转化为一阶近似的线性定解问题。正则模法是将小扰动量分解成一系列模态的叠加(比如Fourier级数形式),使每个模态都满足线性系统,从而将线性定解问题转化为求解广义特征值问题。正则模法适用于具有对称性的流场,根据小扰动的演化情况,可以分为时间模式、空间模式和时空模式。本文回顾了射流及复合射流线性不稳定性分析方法的主要内容和具体实施步骤,并选取流动聚焦这一代表性的微细射流生成技术,概述了线性不稳定性分析方法在实际中的应用,最后对已取得的相关成果进行了总结。
Linear instability analysis is one of the most commonly used theoretical methods for investigating the breakup of single jet and compound jets with cylindrical shapes.The method employs the linearized small perturbations and the normal mode method based on the governing equations and boundary conditions of fluid dynamics to perform relevant investigations,and is able to predict different flow phenomena and rules observed in experiments.The principle of linearized small perturbation method can be characterized by decomposing physical quantities involved in nonlinear problems into zero-order approximations and small perturbations,substituting the results into the original nonlinear equations and omitting the high-order small quantities.Thus the nonlinear problems can be transformed into the first-order approximation of linear definite solution problem.The normal mode method is to decompose small disturbances into a series of modal superposition that meets the linear system.In this way,the problem of linear definite solution is transformed into the problem of solving generalized eigenvalue problem.The normal mode method is suitable for symmetric flow fields and can be divided into different modes in temporal domain,in spatial domain,and in spatio-temporal domain according to the evolution of small disturbances.In this review,the main content and the specific implementation steps of the linear instability analysis method on single jet and compound jets are analyzed.Taking the flow focusing that can generate microjets as an example,the practical applications of the linear instability analysis method are discussed.Finally,the related achievements are also summarized.
Linear instability analysis is one of the most commonly used theoretical methods for investigating the breakup of single jet and compound jets with cylindrical shapes.The method employs the linearized small perturbations and the normal mode method based on the governing equations and boundary conditions of fluid dynamics to perform relevant investigations,and is able to predict different flow phenomena and rules observed in experiments.The principle of linearized small perturbation method can be characterized by decomposing physical quantities involved in nonlinear problems into zero-order approximations and small perturbations,substituting the results into the original nonlinear equations and omitting the high-order small quantities.Thus the nonlinear problems can be transformed into the first-order approximation of linear definite solution problem.The normal mode method is to decompose small disturbances into a series of modal superposition that meets the linear system.In this way,the problem of linear definite solution is transformed into the problem of solving generalized eigenvalue problem.The normal mode method is suitable for symmetric flow fields and can be divided into different modes in temporal domain,in spatial domain,and in spatio-temporal domain according to the evolution of small disturbances.In this review,the main content and the specific implementation steps of the linear instability analysis method on single jet and compound jets are analyzed.Taking the flow focusing that can generate microjets as an example,the practical applications of the linear instability analysis method are discussed.Finally,the related achievements are also summarized.
引文
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[29]LASHERAS J C,HOPFINGER E J.Liquid jet instability and atomization in a coaxial gas stream[J].Annual Review of Fluid Mechanics,2000,32(1):275-308.
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[31]YECKO P,ZALESKI S,FULLANA J M.Viscous modes in two-phase mixing layers[J].Physics of Fluids,2002,14(12):4115-4122.
[32]BOECK T,ZALESKI S.Viscous versus inviscid instability of two-phase mixing layers with continuous velocity profile[J].Physics of Fluids,2005,17(3):032106.
[33]SEVILLA A,GORDILLO J M.Martínez-Bazán C.The effect of the diameter ratio on the absolute and convective instability of free coflowing jets[J].Physics of Fluids,2002,14(9):3028-3038.
[34]苏海容.自由射流界面稳定性的伪谱分析[D].上海:上海大学,2003.
[35]李芳.同轴带点射流的稳定性研究[D].合肥:中国科学技术大学,2007.LI F.Instability of an electrified coaxial jet[D].Hefei:University of Science and Technology of China,2007.(in Chinese)
[36]司廷.流动聚焦的实验和理论研究[D].合肥:中国科学技术大学,2009.SI T.Experimental and theoretical investigation on flow focusing[D].Hefei:University of Science and Technology of China,2009.(in Chinese)
[37]李广滨.复合流动聚焦的实验和理论研究[D].合肥:中国科学技术大学,2016.LI G B.Experimental and theoretical investigation on compound flow focusing[D].Hefei:University of Science and Technology of China,2016.(in Chinese)
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